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3 years ago

6(7x=8) + 6 = -168 solve variable

Mathematics

1 answer:

Rus_ich [418]3 years ago

5 0

Answer:

1/3 ?

Step-by-step explanation:

im sorry its probably wrong, delete this if it is.

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Find the 10th term of the sequence 1,10,19,28,...

Rainbow [258]

For the first one the nth term is 9n - 8 so the 10th term is 9x10 - 8 = 90-8 = 82

For the second one the nth term is ⅓n + ⅓ so the 11th term is ⅓x11 +⅓ = 3.9999 = 4

5 0

3 years ago

A cab company offers a special discount on fare to senior citizens. The following expression models the average amount a cab dri

steposvetlana [31]

Answer:

D. The constant 250 represents the average collection when no seniors ride.

Step-by-step explanation:

A -- the entire expression represents the driver's pay, not just the constant 250.

B -- collections continue to increase as x goes up, so 250 is the minimum, not the maximum.

C -- x is the number of seniors; 250 is in units of collections (dollars?), not numbers of seniors.

D -- indeed, 250 is the "y-intercept" of the expression, hence the collection when no seniors ride.

4 0

3 years ago

Use calculus to find the largest possible area for a rectangular field that can be enclosed with a fence that is 500 meters long

rewona [7]

Let $x$ and $y$ be the sides of the rectangle. The perimeter is given to be 500m, so we are maximizing the area function $A(x,y)=xy$ subject to the constraint $2x+2y=500$ .

From the constraint, we find

$2x+2y=500\implies x+y=250\implies y=250-x$

so we can write the area function independently of $y$ :

$A(x,y)=\hat A(x)=x(250-x)=250x-x^2$

Differentiating and setting equal to zero, we find one critical point:

$\dfrac{\mathrm d\hat A(x)}{\mathrm dx}=250-2x=0\implies x=125$

which means $y=250-125=125$ , so in fact the largest area is achieved with a square fence that surrounds an area of $A(125,125)=125^2=15625\text{ m}^2$ .

7 0

3 years ago

15.5 × [(2 × 2.4) + 3.2] – 24

scZoUnD [109]

Answer:100

Step-by-step explanation:

2 x 2.4=4.8

4.8+3.2=8.0

15.5 x 8.0=124.00

124.00-24=

100

6 0

3 years ago

Integrate sin^-1(x) dx<br><br> please explain how to do it aswell ...?

Lynna [10]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2264253

_______________

Evaluate the indefinite integral:

$\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx\qquad\quad\checkmark}$

Trigonometric substitution:

$\mathsf{\theta=sin^{-1}(x)\qquad\qquad\dfrac{\pi}{2}\le \theta\le \dfrac{\pi}{2}}$

then,

$\begin{array}{lcl} \mathsf{x=sin\,\theta}&\quad\Rightarrow\quad&\mathsf{dx=cos\,\theta\,d\theta\qquad\checkmark}\\\\\\ &&\mathsf{x^2=sin^2\,\theta}\\\\ &&\mathsf{x^2=1-cos^2\,\theta}\\\\ &&\mathsf{cos^2\,\theta=1-x^2}\\\\ &&\mathsf{cos\,\theta=\sqrt{1-x^2}\qquad\checkmark}\\\\\\ &&\textsf{because }\mathsf{cos\,\theta}\textsf{ is positive for }\mathsf{\theta\in \left[\dfrac{\pi}{2},\,\dfrac{\pi}{2}\right].} \end{array}$

So the integral $\mathsf{(ii)}$ becomes

$\mathsf{=\displaystyle\int\! \theta\,cos\,\theta\,d\theta\qquad\quad(ii)}$

Integrate $\mathsf{(ii)}$ by parts:

$\begin{array}{lcl} \mathsf{u=\theta}&\quad\Rightarrow\quad&\mathsf{du=d\theta}\\\\ \mathsf{dv=cos\,\theta\,d\theta}&\quad\Leftarrow\quad&\mathsf{v=sin\,\theta} \end{array}\\\\\\\\ \mathsf{\displaystyle\int\!u\,dv=u\cdot v-\int\!v\,du}\\\\\\ \mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta-\int\!sin\,\theta\,d\theta}\\\\\\ \mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta-(-cos\,\theta)+C}$

$\mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta+cos\,\theta+C}$

Substitute back for the variable x, and you get

$\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx=sin^{-1}(x)\cdot x+\sqrt{1-x^2}+C}\\\\\\\\ \therefore~~\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx=x\cdot\,sin^{-1}(x)+\sqrt{1-x^2}+C\qquad\quad\checkmark}$

I hope this helps. =)

Tags: <em>integral inverse sine function angle arcsin sine sin trigonometric trig substitution differential integral calculus</em>

6 0

3 years ago